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History of mathematical modelling on financial markets
Cigán, Martin ; Brada, Jaroslav (advisor) ; Langer, Miroslav (referee)
The main goal of this thesis is to introduce the reader to the evolution of some of the well-known mathematical models used in the valuation of investment instruments. The first chapter deals with some of the basic terms used in the following text. The next chapters introduce mathematical models, which are used to valuate stocks, bonds and derivatives. Each chapter contains also a brief description of the instrument itself and in some cases the methods used to evaluate the instruments before the introduction of models. The thesis contains a chapter on concept of portfolio due to its importance in the development of mathematical modelling in this field.
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Analysis of guaranteed investment funds
Mach, Jonáš ; Witzany, Jiří (advisor) ; Stádník, Bohumil (referee)
This thesis focuses on guaranteed investment funds, which have become very popular among investors in the Czech Republic in recent years. The reason for this popularity is the conservativeness of a typical domestic investor, who appreciates the lower bound for the value of his investment. Guaranteed funds characteristically have a complex structure and valuation of their profitability based solely on intuition is therefore impossible. This analysis tries to provide an answer to the question if investing in these funds is reasonable. A large part of the thesis is dedicated to the option theory and option valuation methods, including the famous Black-Scholes formula, as guaranteed investment funds have the characteristics of an option. Thanks to the complicated structure of these products, the analysis itself is done by Monte Carlo simulation.
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Implied Volatility and Smile
Rojček, Jakub ; Pígl, Jan (advisor)
In this work author speaks a little in generic about financial derivatives. Then he derives the famous Black-Scholes formula using less precise mathematical apparatus. Afterwards, he will analyze a few volatility models and their applications for creating volatility surface, which is the main goal of both theoreticians and practitioners. As we will see, the theory is yet very deep but unconsolidated. Nevertheless, praxis has gained some nearly sufficient approaches.
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